RU2818373C1 - Signal-noise environment simulation method - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention relates to a method of simulating a signal-noise environment. To simulate a signal-noise environment, a table-specified energy characteristic of the reproduced signal is entered, or an expression corresponding to its discretized analytical representation is set in the program, accuracy of signal simulation is adjusted based on the number of readings, simulation parameters are selected and calculated in a certain manner.

EFFECT: higher accuracy of simulation and reduced computational complexity of simulation algorithms.

1 cl, 2 dwg, 3 tbl

Description

The invention relates to the field of radio engineering and can be used in semi-natural testing of radio engineering equipment (RTS), as well as in their simulation and training equipment to simulate a signal-interference environment, functional diagnostic control and calculation training.

Modern radio systems are capable of detecting and tracking airborne objects in various climatic conditions, in stationary and dynamic states under the influence of vibrations and pitching, in wide ranges of height, azimuth and speed, in complex active and passive interference environments, including reflection of the probing signal from various types underlying surfaces and hydrometeors. In this case, multi-channel work is possible both on single objects and on group targets. Due to these factors, increased requirements for accuracy and speed are placed on RTS. To satisfy them, a set of test models of environmental signals is required, providing adequate modeling of the operating modes of the RTS and built on the basis of known physical laws and mathematical transformations traditionally used in digital signal processing, as well as data from field experiments. To form a set of testing processes, models and algorithms for simulating deterministic and random signals are used.

Many of the existing models and algorithms do not provide the implementation of processes with energy characteristics of arbitrary shape, including those obtained experimentally. In particular, correlation functions and functions of power spectral density (dispersion) of such random processes may contain outliers or discontinuities of the first kind [1]. The same models and algorithms that make it possible to reproduce such random signals either have high computational complexity or contain transient processes. Such disadvantages of the known approaches make it difficult or impossible to use them for extensive testing of existing and future RTS modes in real time when it is necessary to reproduce a complex signal-interference environment.

These circumstances lead to a decrease in the efficiency of simulating the external environment during semi-natural testing and testing of ground-based RTS.

There is a known method for simulating a random process based on expansions in a trigonometric Fourier series based on the representation of a signal as a sum of sine and cosine functions, which can be used to simulate an air-interference situation in a radio station and adopted as a prototype [2 p. 292-298]. It consists of two stages. Its essence is as follows:

1. Pre-configuration stage, including:

- input of characteristics of the reproduced signal;

- setting the accuracy of the simulation of a random process, controlled by the number N of its samples, selecting or calculating simulation parameters;

- calculation of trigonometric coefficients (spectral coefficients in a trigonometric basis);

2. Stage of signal recovery from the spectrum.

The disadvantages of the considered prototype include the following:

1. The method requires performing N ² addition and multiplication operations and 2 N ² + N memory cells for storing the values of variances and trigonometric functions, as well as the cost of generating N random variables, which causes large expenditures of computing resources.

2. The impossibility of simulating signals specified by spectral density functions (SDFs), autocorrelation functions (ACFs), with outliers and/or discontinuities of the first kind.

3. Long time for simulating processes due to the large number of arithmetic operations inherent in this method.

The technical result of the present invention is the ability to simulate signals specified by the FSP (ACF), while maintaining the accuracy of the simulation in the rigid model time of the RTS and reducing the computational complexity of the simulation algorithms.

The technical result is achieved by the fact that in the method of simulating a signal-interference environment, which consists of preliminary tuning, including entering a tabulated energy characteristic of the reproduced signal or specifying in the program an expression corresponding to its discretized analytical representation, setting the accuracy of the signal simulation, controlled by the number N of its samples, selection or calculation of simulation parameters, calculation of trigonometric coefficients and direct simulation of the signal, including reconstruction of the signal from the spectrum, according to the invention, with preliminary tuning after calculating the trigonometric coefficients, the elements of the Fourier kernel of the operator of interconversion of spectra between the Fourier and Walsh-Paley bases are calculated, highlighting in this core of independent groups of trigonometric coefficients, transforming the spectrum in the trigonometric basis into the spectrum in the Walsh-Paley basis by calculating random Walsh-Paley coefficients, and with direct simulation, the signal is restored from the spectrum by summing the products of ready-made group trigonometric coefficients by group values of random Walsh-Paley coefficients .

The physical essence of the proposed method is as follows. At the first stage, preliminary configuration is carried out, which includes:

Entering initial data, tabulated energy characteristics of the signal (FSPD, ACF) or specifying in the program an expression corresponding to its discretized analytical representation (Table 1).

Table 1. Analytically specified random processes No. FSPD S (ω) ACF R (τ) Name Schedule Analytical entry 1. Physical white noise 2. Exponential 3. Piecewise linear
"triangular"

where S (ω) is the dispersion spectral density function (DSDF);

- correlation function;

τ - time;

- implementation frequency.

Next, the accuracy of the signal simulation is adjusted, regulated by the number N of its samples, which directly affects the accuracy of the simulation.

Next, the simulation parameters are selected or calculated depending on the types of processes being simulated and the algorithm used to simulate:

n is the bit length of the argument representation and the number of the basic function;

T - simulation time;

Δ t _k - time sampling step;

N is the number of signal realizations (samples);

- dispersion;

ω _с - cutoff frequency;

for a table-specified initial ACF: input of an array of its discrete values N .

Next, the trigonometric coefficients are calculated:

(1)

where X _PF ( k ) are trigonometric spectral coefficients calculated from discrete FSPD or discrete ACF;

R _T ( m ) is the theoretical ACF.

The spectra of the same signal, represented in a common functional space by expansions in different basis systems, are always related to each other by a linear transformation operator, which is completely determined by its Fourier kernel [1]. Therefore, further calculation of the elements of the Fourier kernel ( F _H , F _N ) is carried out based on the calculation of the trigonometric Fourier spectrum:

(2)

where pal is the Walsh-Paley function.

For each i -th sample of a discrete random signal, the algorithm requires the calculation of a series, the number of elements of which depends on the number of groups n +1, which is logarithmically less than N ;

The trigonometric spectrum is composite and represents an alternation of even _FN (cosine) and odd _FN (sine) components. The elements of the Fourier kernel, the operator transforming the trigonometric spectrum into the Walsh–Paley spectrum ( pal ), are also divided into even and odd.

Since the signal power is equal to the sum of the powers of its projections [1, 3], the correctness of the spectral transformations carried out can be checked using Parseval’s equality. Equality expresses the squared norm of an element in such a space through the squared moduli of the Fourier coefficients of this element in a given orthogonal system.

Since the selected groups of spectral coefficients are independent, within each group the signal power in both the trigonometric basis and the Walsh-Paley basis is the same. Consequently, Parseval’s equalities can be written in groups and, accordingly, independent groups of spectral coefficients can be identified:

- for group 1:

- for group 2:

- for group number λ, λ=3,4,…, n +1:

l =0.1,…,2 ^{λ -2} -1

where Y _P is the Walsh-Paley random spectrum; Y _PM are even and Y _TN are odd.

These equalities indicate that the distribution of signal power across groups of coefficients is the same when representing the signal in a trigonometric basis and in a Walsh-Paley basis.

Calculation using the above formulas allows us to obtain the Fourier kernel for any N = 2 n .

Calculations have shown that a significant part of the elements of the Fourier kernel matrix is equal to zero. This also occurs in the general case, for arbitrary values of N. To reduce the computational complexity of the process of transforming spectra, it is necessary to avoid performing arithmetic operations that are performed in vain, i.e. over zero elements. In addition, trivial multiplication by an element equal to ±1 should also not be performed, but only lead to a change in the sign of the operand. When implementing simulation algorithms in software, such situations are easily monitored and provide additional savings in transformation time.

Next, the spectrum in the trigonometric basis is converted into a spectrum in the Walsh-Paley basis by calculating the random Walsh-Paley coefficients:

(3)

From expression ( _{3) it is clear that the values of ZH and ZH ,} which for each group λ and each value of the index variables m , l are the product of the corresponding spectral coefficient and element of the Fourier kernel, can also be calculated at the setup stage, stored in computer memory and used in finished form at the stage of direct signal reproduction. As a result, a significant amount of computational operations will be assigned to the setup stage, significantly reducing the computational complexity of the direct signal simulation stage.

Next, the signal is directly simulated, including the reconstruction of the signal from the spectrum using signal simulation in the Walsh-Paley basis. It is represented by the following formula for reconstructing the signal from the spectrum in the Walsh-Paley basis system [3]:

(4)

The stage of direct simulation is reduced in this case to the summation of the products of ready-made group trigonometric coefficients Y _P by group values of the Walsh-Paley basis functions.

, (5)

λ=3.4,…, n +1, l =0.1,…,2λ-2-1.

Multiplication operations are completely eliminated at the stage of direct simulation. A random change of signs is ensured by the same previously introduced uncorrelated random variables μ and γ with a generalized indication introduced for them: And , where the expression (1+2 m ) determines the number of the quantity, and the expression N /(2λ-1) assigns it to the corresponding group.

Thus, by bringing almost all the main computational operations to the setup stage, and when performing them in groups, as well as reducing the series for each i -th signal sample to the number of terms depending on the number of groups, and not on the number of samples, the total number of operations performed at the stage of direct signal simulation is reduced to a minimum.

The invention is illustrated by the following drawings.

In fig. Figure 1 shows a block diagram of the proposed method, which includes the following symbols:

- A1 - Block for setting simulation parameters;

- A2 - Block for calculating the spectrum in the basis of trigonometric functions (TF)

- A3 - Block for converting the spectrum into the Walsh-Paley basis;

- A4 - Block for obtaining a random spectrum;

- A5 - Block for restoring a random signal from the spectrum;

- A6 - Block for calculating the theoretical ACF;

- A7 - Algorithmic ACF calculation block;

- A8 - Experimental ACF calculation block;

- A9 - Graphing block;

- A10 - ACF error calculation block;

- A11 - Spectrum transformation operator block;

- A12 - Block for calculating Walsh functions;

- P1 - order of the Fourier kernel (number of samples, power of the source and target systems of basis functions);

- P2 - deterministic spectrum of the signal in the TF basis;

- P3 - signal spectrum in the Walsh-Paley basis, obtained using a direct or optimized spectrum transformation operator;

- P4 - random spectrum of the signal in the Walsh-Paley basis;

- P5 - spectrum transformation equations;

- P6 - values of Walsh functions in the Paley ordering.

- I1 - energy characteristic of the signal (FSPD or ACF) in tabular (discrete) or analytical representation;

- I2 - number of samples N , which directly affects the accuracy of the simulation;

- I3 - vector of parameters depending on the specified requirements for simulation ( T , Δ t _k , σ _c , ω _c , n number of signal realizations).

- R1 - vector of values of the reproduced signal;

- R2 - vector of theoretical ACF values;

- R3 - vector of values of the algorithmic ACF;

- R4 - vector of experimental ACF values;

- R5 - graph of the reproduced signal;

- R6 - ACF graphs;

- R7 - ACF error values.

- M1 - random number sensor with a given distribution law;

- M2 - function graph builder.

In fig. Figure 2 shows graphs of the dependence of ACF errors on the number of samples of the simulated physical white noise signal, exponential and piecewise linear (“triangular”).

The implementation of the method consists in sequentially performing the following operations:

1. Discretization of the given energy characteristic of the signal is performed before starting work, discrete values are supplied to input I 1. Input data and parameters I i, i =1.3, as well as modeling results Rj , j =1.7 in accordance with expressions (1 -3). In this case, block A1 fully implements the stage of specifying the initial data and simulation parameters, and blocks A6 - A10 are responsible for assessing the quality of the simulation algorithm based on the results of signal reproduction. The calculation of three types of ACF occurs in separate functional blocks A6 - A8, after which the results enter the procedures for plotting ACF and signal graphs (block A9) and determining errors (block A10).

2. In block A2, discrete spectral coefficients are calculated in a trigonometric basis, then the spectrum is converted to the Walsh-Paley basis (block A3), and direct or optimized spectrum transformation operators (block A11) serve as a functional mechanism for spectral transformation.

3. Using a random number sensor (mechanism M1), random variables μ, γ are generated to simulate stationary signals, a random spectrum is formed (block A4), from which a random signal is restored using transformations in the Walsh-Paley basis (block A5).

As a result of simulation modeling in the Matlab environment using the proposed method, it was established that the proposed method not only does not degrade the accuracy of signal reproduction, but also has a slightly higher simulation accuracy in terms of the error of the experimental ACF.

For the purpose of conducting a computational experiment, three analytically specified FSPDs of non-rational form and the corresponding autocorrelation functions were selected: physical white noise, exponential and piecewise linear (“triangular”). These characteristics are used in practice, are well studied [1,3] and can serve as test ones when testing algorithms for simulating random processes presented in Table 1.

Parameters for simulating physical white noise: N =128, ω _c =10π, b =0.5, σ=1. The dispersion value is taken equal to unity for the convenience of subsequent comparison and evaluation of errors obtained by the ACF of the simulated signals.

Parameters for simulating exponential and piecewise linear functions N =128, ω _c =10π, σ=1: Discretization parameter b for exponential FSPD is taken equal to 0.001, for “triangular” - 0.5.

Practical modeling has shown that the newly developed algorithm not only does not degrade the accuracy of signal reproduction, but also has a slightly higher simulation accuracy in terms of the error of the experimental ACF. On the applied FSPDs, with a sufficient number of readings N=128 for practical purposes, the reduction in the indicated error amounted to a value from 0.002 to 0.03. The average reduction in error during simulation on the same FSPD and N values from 32 to 1024 has a spread from 0.0005 to 0.0152 (Fig. 2).

The analysis of all the main stages of simulating algorithms based on Fourier and Walsh-Paley, presented in Table 2, showed a time gain coefficient on average of more than 20% (which indicates a reduction in signal simulation time), which makes it possible to simulate signal-interference signals in a rigid model time RTS situation.

Table 2. Analysis of all main stages of simulation of algorithms based on Fourier and Walsh-Paley

Analytical assessment time computational complexity of the developed simulation method, presented in Table 3, which showed the advantage of simulation in the Walsh-Paley basis over simulation in the basis of trigonometric functions. Compared to them, the computational complexity of algorithms for simulating stationary signals has been reduced by at least 1.2 times.

Thus, the developed method for simulating a signal-noise environment makes it possible to simulate the signal-noise environment of an RTS in a rigid model time and reduce the computational complexity of simulation algorithms during semi-natural tests.

The proposed method is industrially applicable, since it is based on well-known achievements in radio-electronic technology and does not require changes to the design of the radar complex.

List of sources used

1. Zalmanzon L.A. Fourier, Walsh, Haar transforms and their application in control, communications and other areas. M.: Science. 1989. 496 p.

2. Pugachev V.S. Theory of random functions and its application to automatic control problems. 3rd ed., rev. M.: Fizmatgiz. 1962. 883 p.

3. Algorithms for transforming spectra in Hartley and Walsh bases / Proletarsky A.V. [etc.] // Automation. Modern technologies. M.: Publishing house "Innovative mechanical engineering". 2018. T. 72, No. 10. P. 453-461.

4. Winograd S. On the calculation of the discrete Fourier transform // McClellan J.G., Rader Ch.M. Application of number theory in digital signal processing. M.: Radio and communications. 1983. pp. 117-136.

Claims (1)

A method of simulating a signal-interference environment, which consists of preliminary setup, including entering a tabulated energy characteristic of the reproduced signal or specifying in the program an expression corresponding to its discretized analytical representation, setting the accuracy of signal simulation, adjustable by the number N of its samples, selecting or calculating simulation parameters, calculation trigonometric coefficients and direct signal simulation, including reconstruction of the signal from the spectrum, characterized in that during preliminary setup, after calculating the trigonometric coefficients, the elements of the Fourier kernel of the operator of interconversion of spectra between the Fourier and Walsh-Paley bases are calculated, independent groups of trigonometric coefficients are identified in this kernel, transformation spectrum in a trigonometric basis into a spectrum in a Walsh-Paley basis by calculating random Walsh-Paley coefficients, and with direct simulation, the signal is restored from the spectrum by summing the products of ready-made group trigonometric coefficients by group values of random Walsh-Paley coefficients.